\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t34\_comptrig (TMErdJwLWgozZv9K19ZCwVdh5gPUii9UTjf)}
\maketitle
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_comptrig : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ k17\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k21\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_complex1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}((\\
\preoh (X0{\unicdcdgdad}X1){\unicdcdcdhd}(r1\_xxreal\_0~(k17\_complex1~(k6\_xcmplx\_0~X0~X1))~k6\_numbers)){\unicdcdcdhd}\\
(\preoh (\preoh r1\_xxreal\_0~(k17\_complex1~(k6\_xcmplx\_0~X0~X1))~k6\_numbers){\unicdcdcdhd}\\
(X0=X1))))\end{array}
\label{hyp:ehgdcdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}((\\
k17\_complex1~(k6\_xcmplx\_0~X0~X1)=k6\_numbers){\unicdbdjded}(X0=X1)))\end{array}
\label{hyp:ehgdbdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh r1\_xxreal\_0~(k10\_real\_1~k32\_sin\_cos~np\_\_2)~k6\_numbers){\unicdcdcdhd}((\\
\preoh r1\_xxreal\_0~k32\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2)){\unicdcdcdhd}((\\
\preoh r1\_xxreal\_0~k32\_sin\_cos~k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k10\_real\_1~\\
k32\_sin\_cos~np\_\_2)~(k1\_real\_1~(k10\_real\_1~k32\_sin\_cos~np\_\_2))){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~(k8\_real\_1~np\_\_2~k32\_sin\_cos)~k32\_sin\_cos){\unicdcdcdhd}(\\
(\preoh r1\_xxreal\_0~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_2)~k32\_sin\_cos)~\\
(k10\_real\_1~k32\_sin\_cos~np\_\_2)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~k6\_numbers~(\\
k1\_real\_1~(k10\_real\_1~k32\_sin\_cos~np\_\_2))){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(\\
k8\_real\_1~np\_\_2~k32\_sin\_cos)~k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k8\_real\_1~\\
(k10\_real\_1~np\_\_3~np\_\_2)~k32\_sin\_cos)~k32\_sin\_cos){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k8\_real\_1~np\_\_2~k32\_sin\_cos)~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_2)~\\
k32\_sin\_cos)){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_2)~\\
k32\_sin\_cos)~k6\_numbers))))))))))\end{array}
\label{hyp:ehfdpfdgpgngahehchjghg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k6\_xcmplx\_0}~{X0}}~{X0}}={k6\_numbers}})}}}\label{hyp:ehbdedpfihdgngahmgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}\label{hyp:mgbdjdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k1\_comptrig~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfdgpgngahehchjghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
(((X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}((X1=k1\_comptrig~X0){\unicdbdjded}((X0=k2\_xcmplx\_0~(\\
k8\_real\_1~(k17\_complex1~X0)~(k21\_sin\_cos~X1))~(k3\_xcmplx\_0~(k8\_real\_1~\\
(k17\_complex1~X0)~(k18\_sin\_cos~X1))~k7\_complex1)){\unicdcdcdhd}((r1\_xxreal\_0~\\
k6\_numbers~X1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k8\_real\_1~np\_\_2~k32\_sin\_cos)~X1))))){\unicdcdcdhd}\\
((X0=k6\_numbers){\unicdbdjdcd}((X1=k1\_comptrig~X0){\unicdbdjded}(X1=k6\_numbers)))))\end{array}
\label{hyp:egbdpfdgpgngahehchjghg}
\end{equation}
\begin{theorem}\label{thm:ehddedpfdgpgngahehchjghg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~(k1\_comptrig~\\
X0)){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k8\_real\_1~np\_\_2~k32\_sin\_cos)~(k1\_comptrig~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
